A hybrid iterative scheme for mixed equilibrium problems, general system of variational inequality problems, and fixed point problems in Hilbert spaces
type: Item
instance of: scholarly article
title: A hybrid iterative scheme for mixed equilibrium problems, general system of variational inequality problems, and fixed point problems in Hilbert spaces
zbMATH Open document ID: 1296.47077
DOI: 10.5402/2011/837809
author: Suthep Suantai
author: Suwicha Imnang
published in: ISRN Mathematical Analysis
publication date: 2011-10-27T00:00:00Z
review text: Summary: We introduce a new iterative scheme for finding a common element of the set of solutions of a general system of variational inequalities, the set of solutions of a mixed equilibrium problem, and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Using the demiclosedness principle for nonexpansive mappings, we prove that the iterative sequence converges strongly to a common element of the above three sets under some control conditions, and we also give some examples for mappings which satisfy the conditions of the main result.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47J20
zbMATH DE Number: 5964502
zbMATH Keywords: iterative method
zbMATH Keywords: variational inequalities
zbMATH Keywords: mixed equilibrium problem
zbMATH Keywords: fixed point
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: real Hilbert space
zbMATH Keywords: demiclosedness principle
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2011/837809
OpenAlex ID: W2064098885
Wikidata QID: Q58690016
cites work: Fixed points of nonexpanding maps
cites work: Q4119693
cites work: Q4881791
cites work: Approximation of fixed points of nonexpansive mappings
cites work: Mann-Type Steepest-Descent and Modified Hybrid Steepest-Descent Methods for Variational Inequalities in Banach Spaces
cites work: On relaxed viscosity iterative methods for variational inequalities in Banach spaces
cites work: Existence theorems for generalized vector variational inequalities with pseudomonotonicity and their applications
cites work: Strong weak convergence theorems of implicit hybrid steepest-descent methods for variational inequalities
cites work: Iterative approaches to solving equilibrium problems and fixed point problems of infinitely many nonexpansive mappings
cites work: Q3526317
cites work: Hybrid steepest descent methods for zeros of nonlinear operators with applications to variational inequalities
cites work: Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities
cites work: A hybrid iterative scheme for mixed equilibrium problems and fixed point problems
cites work: Relaxed viscosity approximation methods for fixed point problems and variational inequality problems
cites work: A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization
cites work: On iterative methods for solving a system of mixed variational inequalities
cites work: Projection methods for nonconvex variational inequalities
cites work: Some developments in general variational inequalities
cites work: Q3601254
cites work: A new hybrid-extragradient method for generalized mixed equilibrium problems, fixed point problems and variational inequality problems
cites work: Some new iterative algorithms for generalized mixed equilibrium problems with strict pseudo-contractions and monotone mappings
cites work: A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings
cites work: Modified extragradient methods for a system of variational inequalities in Banach spaces
cites work: A hybrid extragradient method for general variational inequalities
cites work: A new iterative method for equilibrium problems and fixed point problems of infinitely nonexpansive mappings and monotone mappings
cites work: Q4110807
cites work: On modified iterative method for nonexpansive mappings and monotone mappings
cites work: Q4494974
cites work: Q3998720
cites work: Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems
cites work: Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
cites work: Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations
cites work: Hybrid iterative scheme for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings
description: scientific article; zbMATH DE number 5964502